Please submit a html output of your R notebook and include summary statistics and explanation of the variables in the dataset. Also, please include an explanation of your model results.

library(data.table)
library(leaps)

Problem 1

Use the College dataset from ISLR2 library and use best subset selection, forward and backward selection methods to predict the number of applications received using the other variables.

dt <- data.table(ISLR2::College)
head(dt)

The ISLR2::College dataset contains “Statistics for a large number of US Colleges from the 1995 issue of US News and World Report.” If you want to learn more, I suggest visiting https://rdocumentation.org/packages/ISLR2/versions/1.3-1/topics/College.

Summary Stats

summary(dt)
 Private        Apps           Accept          Enroll       Top10perc       Top25perc      F.Undergrad   
 No :212   Min.   :   81   Min.   :   72   Min.   :  35   Min.   : 1.00   Min.   :  9.0   Min.   :  139  
 Yes:565   1st Qu.:  776   1st Qu.:  604   1st Qu.: 242   1st Qu.:15.00   1st Qu.: 41.0   1st Qu.:  992  
           Median : 1558   Median : 1110   Median : 434   Median :23.00   Median : 54.0   Median : 1707  
           Mean   : 3002   Mean   : 2019   Mean   : 780   Mean   :27.56   Mean   : 55.8   Mean   : 3700  
           3rd Qu.: 3624   3rd Qu.: 2424   3rd Qu.: 902   3rd Qu.:35.00   3rd Qu.: 69.0   3rd Qu.: 4005  
           Max.   :48094   Max.   :26330   Max.   :6392   Max.   :96.00   Max.   :100.0   Max.   :31643  
  P.Undergrad         Outstate       Room.Board       Books           Personal         PhD            Terminal    
 Min.   :    1.0   Min.   : 2340   Min.   :1780   Min.   :  96.0   Min.   : 250   Min.   :  8.00   Min.   : 24.0  
 1st Qu.:   95.0   1st Qu.: 7320   1st Qu.:3597   1st Qu.: 470.0   1st Qu.: 850   1st Qu.: 62.00   1st Qu.: 71.0  
 Median :  353.0   Median : 9990   Median :4200   Median : 500.0   Median :1200   Median : 75.00   Median : 82.0  
 Mean   :  855.3   Mean   :10441   Mean   :4358   Mean   : 549.4   Mean   :1341   Mean   : 72.66   Mean   : 79.7  
 3rd Qu.:  967.0   3rd Qu.:12925   3rd Qu.:5050   3rd Qu.: 600.0   3rd Qu.:1700   3rd Qu.: 85.00   3rd Qu.: 92.0  
 Max.   :21836.0   Max.   :21700   Max.   :8124   Max.   :2340.0   Max.   :6800   Max.   :103.00   Max.   :100.0  
   S.F.Ratio      perc.alumni        Expend        Grad.Rate     
 Min.   : 2.50   Min.   : 0.00   Min.   : 3186   Min.   : 10.00  
 1st Qu.:11.50   1st Qu.:13.00   1st Qu.: 6751   1st Qu.: 53.00  
 Median :13.60   Median :21.00   Median : 8377   Median : 65.00  
 Mean   :14.09   Mean   :22.74   Mean   : 9660   Mean   : 65.46  
 3rd Qu.:16.50   3rd Qu.:31.00   3rd Qu.:10830   3rd Qu.: 78.00  
 Max.   :39.80   Max.   :64.00   Max.   :56233   Max.   :118.00  
df <- dewey::ifelsedata(data.frame(round(cor(dt[, !c("Private")]), 3)), 
                        .85, "x >= y & x != 1", matchCols = FALSE)
rownames(df) <- colnames(df)
df
GGally::ggpairs(dt, mapping = ggplot2::aes(color = Private))

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These are the summary statistics. There’s nothing crazy about them in general. Maybe a few outliers. There aren’t a ton of things that are correlated at a rate at or higher than \(85\%\). It is all generally expected.

Normal

best_fit <- regsubsets(Apps ~ ., dt, nvmax = 17)
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))

plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")


normal <- as.formula("Apps ~ + Private + Accept + Enroll + Top10perc + Top25perc + Outstate + Room.Board + PhD + Expend + Grad.Rate")

Forward

best_fit <- regsubsets(Apps ~ ., dt, nvmax = 17, method = "forward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))

plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")


forward <- as.formula("Apps ~ + Private + Accept + Enroll + Top10perc + Top25perc + Outstate + Room.Board + PhD + Expend + Grad.Rate")

Backward

best_fit <- regsubsets(Apps ~ ., dt, nvmax = 17, method = "backward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))

plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")


backward <- as.formula("Apps ~ + Private + Accept + Enroll + Top10perc + Top25perc + Outstate + Room.Board + PhD + Expend + Grad.Rate")

Conclusion

regs <- dewey::regsearch(dt, "Apps", colnames(dt[, !c("Apps")]), 1, 10, "gaussian", 0, FALSE, TRUE)
[1] "Assembling regresions..."

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[1] "Creating 109293 formulas. Please be patient, this may take a while."
[1] "Creating regressions..."

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[1] "Running 109293 regressions. Please be patient, this may take a while."
[1] "Running regressions..."

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regs

dewey <- as.formula("Apps ~ + Accept + Top10perc")
# regsubsets produced the same arguments
forms <- c(normal, dewey)

lapply(forms, function(x) { summary(lm(formula = x, dt)) })
[[1]]

Call:
lm(formula = x, data = dt)

Residuals:
    Min      1Q  Median      3Q     Max 
-5085.2  -439.2   -27.4   315.6  7848.6 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -100.51668  265.47592  -0.379 0.705069    
PrivateYes  -575.07061  132.52820  -4.339 1.62e-05 ***
Accept         1.58422    0.04011  39.500  < 2e-16 ***
Enroll        -0.56221    0.11091  -5.069 5.02e-07 ***
Top10perc     49.13909    5.51638   8.908  < 2e-16 ***
Top25perc    -13.86531    4.41751  -3.139 0.001762 ** 
Outstate      -0.09466    0.01829  -5.176 2.89e-07 ***
Room.Board     0.16374    0.04668   3.508 0.000478 ***
PhD          -10.01609    3.11921  -3.211 0.001378 ** 
Expend         0.07274    0.01142   6.370 3.26e-10 ***
Grad.Rate      7.33269    2.82114   2.599 0.009524 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1043 on 766 degrees of freedom
Multiple R-squared:  0.9283,    Adjusted R-squared:  0.9274 
F-statistic: 991.9 on 10 and 766 DF,  p-value: < 2.2e-16


[[2]]

Call:
lm(formula = x, data = dt)

Residuals:
    Min      1Q  Median      3Q     Max 
-5334.2  -513.9   -16.7   325.1  9780.8 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -892.97561   77.89816  -11.46   <2e-16 ***
Accept         1.44004    0.01678   85.80   <2e-16 ***
Top10perc     35.83112    2.33210   15.36   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1125 on 774 degrees of freedom
Multiple R-squared:  0.9158,    Adjusted R-squared:  0.9156 
F-statistic:  4208 on 2 and 774 DF,  p-value: < 2.2e-16

The model from regsubsets is a little bit more accurate but comes at the cost of needing to include many more variables. If data collection was no issue, the regsubsets one is good, if data collection is an issue, then mine is much better. Basically, as the number of applications accepted increases by one, the number of applications received increases by \(1.44\). As the percent of new students that were in the top 10% of their high school class increases by one, the number of applications received increases by \(35.83\).

Problem 2

Use the Boston data to predict the per capita crime rate using best subset selection, forward and backward selection methods.

dt <- data.table(ISLR2::Boston)
head(dt)

The ISLR2::Boston dataset contains “A data set containing housing values in 506 suburbs of Boston.” If you want to learn more, I suggest visiting https://rdocumentation.org/packages/ISLR2/versions/1.3-1/topics/Boston.

Summary Stats

summary(dt)
      crim                zn             indus            chas              nox               rm             age        
 Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000   Min.   :0.3850   Min.   :3.561   Min.   :  2.90  
 1st Qu.: 0.08205   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000   1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02  
 Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000   Median :0.5380   Median :6.208   Median : 77.50  
 Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917   Mean   :0.5547   Mean   :6.285   Mean   : 68.57  
 3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000   3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08  
 Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000   Max.   :0.8710   Max.   :8.780   Max.   :100.00  
      dis              rad              tax           ptratio          lstat            medv      
 Min.   : 1.130   Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   : 1.73   Min.   : 5.00  
 1st Qu.: 2.100   1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.: 6.95   1st Qu.:17.02  
 Median : 3.207   Median : 5.000   Median :330.0   Median :19.05   Median :11.36   Median :21.20  
 Mean   : 3.795   Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :12.65   Mean   :22.53  
 3rd Qu.: 5.188   3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:16.95   3rd Qu.:25.00  
 Max.   :12.127   Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :37.97   Max.   :50.00  
df <- dewey::ifelsedata(data.frame(round(cor(dt), 3)), 
                        .85, "x >= y & x != 1", matchCols = FALSE)
rownames(df) <- colnames(df)
df
GGally::ggpairs(dt)

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There’s nothing crazy with these numbers. It is weird that only tax and rad are correlated above \(85%\), but then again highways decrease property taxes or something. idk.

Normal

best_fit <- regsubsets(crim ~ ., dt, nvmax = 12)
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))

plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")


normal <- as.formula("crim ~ + zn + nox + dis + rad + ptratio + lstat + medv")

Forward

best_fit <- regsubsets(crim ~ ., dt, nvmax = 12, method = "forward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))

plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")


forward <- as.formula("crim ~ + zn + nox + rm + dis + rad + ptratio + lstat + medv")

Backward

best_fit <- regsubsets(crim ~ ., dt, nvmax = 12, method = "backward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))

plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")


backward <- as.formula("crim ~ zn + nox + dis + rad + ptratio + lstat + medv")

Conclusion

regs <- dewey::regsearch(dt, "crim", c(colnames(dt[, !c("crim")]), "lstat*rad"), 1, 12, "gaussian", 0, FALSE, TRUE)
[1] "Assembling regresions..."

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[1] "Creating 8190 formulas. Please be patient, this may take a while."
[1] "Creating regressions..."

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[1] "Running 5119 regressions. Please be patient, this may take a while."
[1] "Running regressions..."

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regs

dewey <- as.formula("crim ~ + lstat + rad")
# regsubsets produced the same arguments for normal and backward
# dropped backward
forms <- c(normal, forward, dewey)

lapply(forms, function(x) { summary(lm(formula = x, dt)) })
[[1]]

Call:
lm(formula = x, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-8.655 -2.143 -0.319  1.050 74.740 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  17.46682    6.02424   2.899 0.003904 ** 
zn            0.04497    0.01803   2.494 0.012951 *  
nox         -12.45782    4.77637  -2.608 0.009375 ** 
dis          -0.94255    0.26270  -3.588 0.000366 ***
rad           0.56152    0.04813  11.667  < 2e-16 ***
ptratio      -0.34703    0.18288  -1.898 0.058322 .  
lstat         0.11479    0.06945   1.653 0.098997 .  
medv         -0.19026    0.05369  -3.543 0.000432 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.452 on 498 degrees of freedom
Multiple R-squared:  0.4452,    Adjusted R-squared:  0.4374 
F-statistic: 57.08 on 7 and 498 DF,  p-value: < 2.2e-16


[[2]]

Call:
lm(formula = x, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-8.724 -2.181 -0.288  1.081 73.947 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  13.25994    6.97229   1.902 0.057774 .  
zn            0.04332    0.01807   2.397 0.016906 *  
nox         -12.50587    4.77446  -2.619 0.009080 ** 
rm            0.70899    0.59233   1.197 0.231896    
dis          -0.93005    0.26279  -3.539 0.000439 ***
rad           0.55378    0.04854  11.409  < 2e-16 ***
ptratio      -0.33823    0.18294  -1.849 0.065079 .  
lstat         0.13578    0.07160   1.896 0.058495 .  
medv         -0.21711    0.05817  -3.732 0.000212 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.449 on 497 degrees of freedom
Multiple R-squared:  0.4467,    Adjusted R-squared:  0.4378 
F-statistic: 50.17 on 8 and 497 DF,  p-value: < 2.2e-16


[[3]]

Call:
lm(formula = x, data = dt)

Residuals:
   Min     1Q Median     3Q    Max 
-8.953 -1.881 -0.249  1.040 76.726 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -4.38141    0.59872  -7.318 1.00e-12 ***
lstat        0.23728    0.04685   5.065 5.75e-07 ***
rad          0.52281    0.03842  13.607  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.559 on 503 degrees of freedom
Multiple R-squared:  0.4208,    Adjusted R-squared:  0.4185 
F-statistic: 182.7 on 2 and 503 DF,  p-value: < 2.2e-16

Again, regsubsets produces slightly better models, but mine is almost as good and is more parsimonious. As lstat increases by one, crim increases by \(.237\) and when rad increases by one, crim increases by \(.522\).

---
title: "Assignment 5"
author: "Gus Lipkin ~ glipkin6737@floridapoly.edu"
output:
  html_notebook:
    toc: true
    toc_depth: 2
    toc_float: true
  pdf_document: default
---

> Please submit a html output of your R notebook and include summary statistics and explanation of the variables in the dataset. Also, please include an explanation of your model results. 

```{r}
library(data.table)
library(leaps)
```

# Problem 1
> Use the College dataset from ISLR2 library and use best subset selection, forward and backward selection methods to predict the number of applications received using the other variables. 

```{r}
dt <- data.table(ISLR2::College)
head(dt)
```

The `ISLR2::College` dataset contains "Statistics for a large number of US Colleges from the 1995 issue of US News and World Report." If you want to learn more, I suggest visiting [https://rdocumentation.org/packages/ISLR2/versions/1.3-1/topics/College](https://rdocumentation.org/packages/ISLR2/versions/1.3-1/topics/College).

## Summary Stats
```{r warning=FALSE}
summary(dt)
df <- dewey::ifelsedata(data.frame(round(cor(dt[, !c("Private")]), 3)), 
                        .85, "x >= y & x != 1", matchCols = FALSE)
rownames(df) <- colnames(df)
df
GGally::ggpairs(dt, mapping = ggplot2::aes(color = Private))
```

These are the summary statistics. There's nothing crazy about them in general. Maybe a few outliers. There aren't a ton of things that are correlated at a rate at or higher than $85\%$. It is all generally expected.

## Normal
```{r}
best_fit <- regsubsets(Apps ~ ., dt, nvmax = 17)
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))
plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")

normal <- as.formula("Apps ~ + Private + Accept + Enroll + Top10perc + Top25perc + Outstate + Room.Board + PhD + Expend + Grad.Rate")
```

## Forward
```{r}
best_fit <- regsubsets(Apps ~ ., dt, nvmax = 17, method = "forward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))
plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")

forward <- as.formula("Apps ~ + Private + Accept + Enroll + Top10perc + Top25perc + Outstate + Room.Board + PhD + Expend + Grad.Rate")
```

## Backward
```{r}
best_fit <- regsubsets(Apps ~ ., dt, nvmax = 17, method = "backward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))
plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")

backward <- as.formula("Apps ~ + Private + Accept + Enroll + Top10perc + Top25perc + Outstate + Room.Board + PhD + Expend + Grad.Rate")
```

## Conclusion
```{r}
regs <- dewey::regsearch(dt, "Apps", colnames(dt[, !c("Apps")]), 1, 10, "gaussian", 0, FALSE, TRUE)
regs

dewey <- as.formula("Apps ~ + Accept + Top10perc")
```

```{r}
# regsubsets produced the same arguments
forms <- c(normal, dewey)

lapply(forms, function(x) { summary(lm(formula = x, dt)) })
```

The model from `regsubsets` is a little bit more accurate but comes at the cost of needing to include many more variables. If data collection was no issue, the `regsubsets` one is good, if data collection is an issue, then mine is much better. Basically, as the number of applications accepted increases by one, the number of applications received increases by $1.44$. As the percent of new students that were in the top 10% of their high school class increases by one, the number of applications received increases by $35.83$.

# Problem 2
> Use the Boston data to predict the per capita crime rate using  best subset selection, forward and backward selection methods.

```{r}
dt <- data.table(ISLR2::Boston)
head(dt)
```

The `ISLR2::Boston` dataset contains "A data set containing housing values in 506 suburbs of Boston." If you want to learn more, I suggest visiting [https://rdocumentation.org/packages/ISLR2/versions/1.3-1/topics/Boston](https://rdocumentation.org/packages/ISLR2/versions/1.3-1/topics/Boston).

## Summary Stats
```{r warning=FALSE}
summary(dt)
df <- dewey::ifelsedata(data.frame(round(cor(dt), 3)), 
                        .85, "x >= y & x != 1", matchCols = FALSE)
rownames(df) <- colnames(df)
df
GGally::ggpairs(dt)
```

There's nothing crazy with these numbers. It is weird that only `tax` and `rad` are correlated above $85%$, but then again highways decrease property taxes or something. idk.

## Normal
```{r}
best_fit <- regsubsets(crim ~ ., dt, nvmax = 12)
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))
plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")

normal <- as.formula("crim ~ + zn + nox + dis + rad + ptratio + lstat + medv")
```

## Forward
```{r}
best_fit <- regsubsets(crim ~ ., dt, nvmax = 12, method = "forward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))
plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")

forward <- as.formula("crim ~ + zn + nox + rm + dis + rad + ptratio + lstat + medv")
```

## Backward
```{r}
best_fit <- regsubsets(crim ~ ., dt, nvmax = 12, method = "backward")
best_summary <- summary(best_fit)

data.table("BIC" = best_summary$bic,
           "Cp" = best_summary$cp,
           "r2" = best_summary$adjr2)[order(r2 * -1, BIC, Cp)]

par(mfrow = c(1,2))
plot(best_summary$cp, xlab = "number of features", ylab = "cp")
plot(best_fit, scale = "Cp")

par(mfrow = c(1, 2))
plot(best_summary$bic, xlab = "number of features", ylab = "bic")
plot(best_fit, scale = "bic")

backward <- as.formula("crim ~ zn + nox + dis + rad + ptratio + lstat + medv")
```

## Conclusion
```{r}
regs <- dewey::regsearch(dt, "crim", c(colnames(dt[, !c("crim")]), "lstat*rad"), 1, 12, "gaussian", 0, FALSE, TRUE)
regs

dewey <- as.formula("crim ~ + lstat + rad")
```

```{r}
# regsubsets produced the same arguments for normal and backward
# dropped backward
forms <- c(normal, forward, dewey)

lapply(forms, function(x) { summary(lm(formula = x, dt)) })
```

Again, `regsubsets` produces slightly better models, but mine is almost as good and is more *parsimonious*. As `lstat` increases by one, `crim` increases by $.237$ and when `rad` increases by one, `crim` increases by $.522$.
